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Bayes Theorum And Probablity of God: No Dice!

Don wrote a great post last time arguing against the use of Bayes Theorem to disprove the resurrection. I thought we could do0 a theme, suma contra Bayes. A couple of years ago I debated Jeff Lowder of secular web on the use of Bayes in arguing against existence of God. This post was what prompted him t o call me out. Next time I'll post my response to his attack.

It is understandable that naturalistic thinkers are uneasy with the concept of miracles. So should we all be watchful not to believe too quickly because its easy to get caught up in private reasons and ignore reason itself. Thus has more than one intelligent person been taken by both scams and honest mistakes. By the the same token it is equally adanger that one will remain too long in the skeptical place and become overly committed to doubting everything. From that position the circular reasoning of the naturalist seems so reasonable. There’s never been any proof of miracles before so we can’t accept that there is any now. But that’s only because we keep making the same assumption and thus have always dismissed the evidence that was valid.

At this point most atheists will interject the ECREE issue (or ECREP—extraordinary claims require extraordinary evidence, or “proof”). That would justify the notion of remaining skeptical about miracle evidence even when its good. There are many refutations of this phrase, which was popularized by Karl Sagan. One of the major problems with this idea is that atheists rarely get around to defining “extraordinary” either in terms of the claim (why would belief in God be extraordinary? 90% of humanity believe in some form of God) [1] The slogan ECREE is usually said to be based upon the Bayes completeness theorem.Sagan popularized the slogan ECREE but the mathematical formula that it is often linked to (but not identical to) was invented by the man whose name it bears, working in theseventeen forties but then he abandoned it, perhaps because mathematicians didn’t like it. It was picked up by the great scientist and atheist Laplace and improved upon.[2] This method affords new atheism the claim of a “scientific/mathematical” procedure that disproves God by demonstrating that God is totally improbable. It is also used to supposedly disprove supernatural effects as well as they are rendered totally improbable.[3]

It is often assumed that the theorem was developed to back up Hume’s argument against miracles. Bayes was trying to argue against Hume and to find a mathematical way to prove that there must be a first cause to the universe.[4] Mathematicians have disapproved of the theorem for most of its existence. It has been rejected on the grounds that it’s based upon guesswork. It was regarded as a parlor trick until World War II then it was regarded as a useful parlor trick. This explains why it was strangely absent from my younger days and early education as a student of the existence of God. I used to pour through philosophy anthologies with God articles in them and never came across it. It was just part of the discussion on the existence of God until about the year 2000 suddenly it’s all over the net. It’s resurgence is primarily due to it’s use by skeptics in trying to argue that God is improbable. It was not taught in math from the end fo the war to the early 90s.[5]

Bayes’ theorem was introduced first as an argument against Hume’s argument on miracles, that is to say, a proof of the probability of miracles. The theorem was learned by Richard Price from Bayes papers after the death of the latter, and was first communicated to the Royal society in 1763.[6] The major difference in the version Bayes and Price used and modern (especially skeptical versions) is that Laplace worked out how to introduce differentiation in prior distributions. The original version gave 50-50 probability to the prior distribution.[7] The problem with using principles such as Bayes theorem is that they can’t tell us what we need to know to make the calculations of probability accurate in dealing with issues where our knowledge is fragmentary and sparse. The theorem is good for dealing with concrete things like tests for cancer, developing spam filters, and military applications but not for determining the answer to questions about reality that are philosophical by nature and that would require an understanding of realms beyond, realms of which we know nothing. Bayes conquered the problem of what level of chance or probability to assign the prior estimate by guessing. This worked because the precept was that future information would come in that would tell him if his guesses were in the ball park or not. Then he could correct them and guess again. As new information came in he would narrow the field to the point where eventually he’s not just in the park but rounding the right base so to speak.

The problem is that doesn’t work as well when no new information comes in, which is what happens when dealing with things beyond human understanding. We don’t have an incoming flood of empirical evidence clarifying the situation with God because God is not the subject of empirical observation. Where we set the prior, which is crucial to the outcome of the whole thing, is always going to be a matter of ideological assumption. For example we could put the prior at 50-50 (either God exists or not) and that would yield a high probability of God.[8] Or the atheist can argue that the odds of God are low because God is not given in the sense data, which is in itself is an ideological assumption. It assumes that the only valid form of knowledge is empirical data. It also ignores several sources of empirical data that can be argued as evidence for God (such as the universal nature of mystical experience).[9] It assumes that God can’t be understood as reality based upon other means of deciding such as personal experience or logic, and it assumes the probability of God is low based upon unbelief because the it could just as easily be assumed as high based upon it’s properly basic nature or some form of elegance (parsimony). In other words this is all a matter of how e chooses to see things. Perspective matters. There is no fortress of facts giving the day to atheism, there is only the prior assumptions one chooses to make and the paradigm under which one chooses to operate; that means the perception one chooses to filter the data through.

Stephen Unwin tries to produce a simple analysis that would prove the ultimate truth of God using Bayes. The calculations he gives for the priors are as such:

Recognition of goodness (D = 10)

Existence of moral evil (D = 0.5)

Existence of natural evil (D = 0.1)

Intra-natural miracles (e.g., a friend recovers from an illness after you have prayed for him) (D = 2)

Extra-natural miracles (e.g., someone who is dead is brought back to life) (D = 1)

This is admittedly subjective, and all one need do is examine it to see this. Why give recognition of moral evil 0.5? If you read C.S. Lewis its obvious if you read B.F. Skinner there’s no such thing. That’s not scientific fact but opinon. When NASA does analysis of gas pockets on moons of Jupiter they don’t start out by saying “now let’s discuss the value system that would allow us to posit the existence of gas.” They are dealing with observable things that must be proved regardless of one’s value system. These questions (setting the prior for God) are matters for theology. The existence of moral evil for example this is not a done deal. This is not a proof or disproof of God. It’s a job for a theologian, not a scientist, to decide why God allows moral evil, or in fact if moral evil exists. These issues are all too touchy to just blithely plug in the conclusions in assessing the prior probability of God. That makes the process of obtaining a probability of God fairly presumptive.

[2] Sharon Berstch McGrayne, The Theory that would not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy. New Haven: Yale University Press, 2011, 3.

Faculty of Business AdministrationSimon Fraser UniversityBurnaby, BCCANADA V5A 1S6. Geoffrey Poitras is a Professor of Finance in the Faculty of Business Administration at SimonFraserUniversity. Lisited 12/22/12.

[8] Joe Carter, “The Probability of God” First Thoughts. Blog of publication of First Things. (August 18, 2010) URL: http://www.firstthings.com/blogs/firstthoughts/2010/08/18/the-probability-of-god/visited (1/10/13). Carter points out that when Unwin (an atheist discussed in previous chapter) puts in 50% prior he gets 67% probability for God. When Cater himself does so he get’s 99%.Cater’s caveat: “Let me clarify that this argument is not intended to be used as a proof of God’s existence. The sole intention is to put in quantifiable terms the probabilities that we should form a belief about such a Being’s existence. In other words, this is not an ontological proof but a means of justifying a particular epistemic stance toward the idea of the existence or non-existence of a deity.The argument is that starting from an epistemically neutral point (50 percent/50 percent), we can factor in specific evidence for the existence or non-existence of a deity. After evaluating each line of evidence, we can determine if it is more or less likely that it would entail the existence of God.”

Comments

Good stuff Joe. I agree that Bayes' Theorem has its limitations. I don't think it's the best way to answer historical questions, for example, let alone deep metaphysical questions.

As I see it the prior probability for just about any significant historical event has to be low, just because significant historical events are usually unprecedented (that's what makes them significant).

Ha! That point, and the broader point about the limited applicability of Bayes' Theorem, are well taken. It's difficult to use evidence to "update" metaphysical beliefs and assumptions whose validity is not based on evidence. I do think skeptics have every right to use Bayesianism against hardcore Christian evidentialism, though I think even then their arguments fail (the point of my post).

I also appreciate your reference to the history on Price's earliest use of Bayes' Theorem to challenge Hume's skepticism (as opposed to the modernist tendency to use Bayes against miracles). The atheistic revisionism that hijacked Bayes' Theorem has done something similar with Occam's Razor. How many internet atheists swamping message boards with appeals to Occam's Razor are aware that Occam was a thoroughgoing theist, and held God to be the only necessary entity?

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